$ \begin{cases}  \frac{CE}{BC} = \frac{CE}{CD+DB} = \frac{6}{4+14} = \frac{6}{18} = \frac{1}{3} \\ \frac{DC}{AC} = \frac{DC}{CE+EA} = \frac{4}{6+6} = \frac{4}{12} = \frac{1}{3} \end{cases} \Rightarrow \frac{CE}{BC} = \frac{DC}{AC} = \frac{1}{3} \\ ABC , DEC : \begin{cases} \hat{c} = \hat{c} \\ \frac{CE}{BC} = \frac{DC}{AC} = \frac{1}{3}  \end{cases} \Rightarrow ABC \sim DEC \Rightarrow \frac{DM}{AN} = \frac{1}{3} \Rightarrow AN=2 \times 3=6 \\ CN=\sqrt{AC^2-AN^2} = \sqrt{12^2-6^2} = \sqrt{144-36} = \sqrt{108} = 6\sqrt{3} \\ BN=BC-CN = 18-6\sqrt{3} = 6(3-\sqrt{3}) $